x uchun yechish (complex solution)
x=\frac{3+\sqrt{15}i}{4}\approx 0,75+0,968245837i
x=\frac{-\sqrt{15}i+3}{4}\approx 0,75-0,968245837i
Grafik
Baham ko'rish
Klipbordga nusxa olish
2x^{2}-3x+3=0
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.
x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2\times 3}}{2\times 2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -3 ni b va 3 ni c bilan almashtiring.
x=\frac{-\left(-3\right)±\sqrt{9-4\times 2\times 3}}{2\times 2}
-3 kvadratini chiqarish.
x=\frac{-\left(-3\right)±\sqrt{9-8\times 3}}{2\times 2}
-4 ni 2 marotabaga ko'paytirish.
x=\frac{-\left(-3\right)±\sqrt{9-24}}{2\times 2}
-8 ni 3 marotabaga ko'paytirish.
x=\frac{-\left(-3\right)±\sqrt{-15}}{2\times 2}
9 ni -24 ga qo'shish.
x=\frac{-\left(-3\right)±\sqrt{15}i}{2\times 2}
-15 ning kvadrat ildizini chiqarish.
x=\frac{3±\sqrt{15}i}{2\times 2}
-3 ning teskarisi 3 ga teng.
x=\frac{3±\sqrt{15}i}{4}
2 ni 2 marotabaga ko'paytirish.
x=\frac{3+\sqrt{15}i}{4}
x=\frac{3±\sqrt{15}i}{4} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{15} ga qo'shish.
x=\frac{-\sqrt{15}i+3}{4}
x=\frac{3±\sqrt{15}i}{4} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{15} ni ayirish.
x=\frac{3+\sqrt{15}i}{4} x=\frac{-\sqrt{15}i+3}{4}
Tenglama yechildi.
2x^{2}-3x+3=0
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
2x^{2}-3x+3-3=-3
Tenglamaning ikkala tarafidan 3 ni ayirish.
2x^{2}-3x=-3
O‘zidan 3 ayirilsa 0 qoladi.
\frac{2x^{2}-3x}{2}=-\frac{3}{2}
Ikki tarafini 2 ga bo‘ling.
x^{2}-\frac{3}{2}x=-\frac{3}{2}
2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.
x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=-\frac{3}{2}+\left(-\frac{3}{4}\right)^{2}
-\frac{3}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{4} olish uchun. Keyin, -\frac{3}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-\frac{3}{2}x+\frac{9}{16}=-\frac{3}{2}+\frac{9}{16}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{4} kvadratini chiqarish.
x^{2}-\frac{3}{2}x+\frac{9}{16}=-\frac{15}{16}
Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{3}{2} ni \frac{9}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.
\left(x-\frac{3}{4}\right)^{2}=-\frac{15}{16}
x^{2}-\frac{3}{2}x+\frac{9}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{-\frac{15}{16}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-\frac{3}{4}=\frac{\sqrt{15}i}{4} x-\frac{3}{4}=-\frac{\sqrt{15}i}{4}
Qisqartirish.
x=\frac{3+\sqrt{15}i}{4} x=\frac{-\sqrt{15}i+3}{4}
\frac{3}{4} ni tenglamaning ikkala tarafiga qo'shish.
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